kruskal.cpp

/* Minimum Spanning Tree - Kruskal */
/* Author : M. A. Rafsan Mazumder */

#include <bits/stdc++.h>

using namespace std;

#define MAX 10000
#define ll long long

pair<ll, pair<int, int> > p[MAX];
int id[MAX];
int nodes, edges;

void initialize()
{
    for(int i=0; i<MAX; i++) id[i] = i;
}

int root(int x)
{
    while(id[x] != x){
        id[x] = id[id[x]];
        x = id[x];
    }
    return x;
}

void union1(int x, int y)
{
    int p = root(x);
    int q = root(y);
    id[p] = id[q];
}

ll kruskal(pair<ll, pair<int, int> > p[])
{
    int x, y;
    ll minimumCost = 0, cost;
    for(int i=0; i<edges; i++){
        x = p[i].second.first;
        y = p[i].second.second;
        cost = p[i].first;

        if(root(x) != root(y)){
            minimumCost += cost;
            union1(x, y);
        }
    }
    return minimumCost;
}

int main()
{
    int x, y;
    long long weight, cost, minimumCost;
    initialize();
    cin >> nodes >> edges;
    for(int i=0; i<edges; i++)
    {
        cin >> x >> y >> weight;
        p[i] = make_pair(weight, make_pair(x, y));
    }
    sort(p, p + edges);
    minimumCost = kruskal(p);
    cout << minimumCost << endl;
    return 0;
}